I have different nail paint colors, but I don't have skin or golden. Is it possible to make these colors by using two or more different nail paints?
The phrase "skin colour" is a bit ambiguous, but mixing all three primary colours or any two complimentary (particularly orange & blue) gives you a great brown that can be lightened with white if necessary. Here's a WikiHow about it.
Gold would be really hard, because you want it to reflect light. If your starting colours aren't reflective, it'll never look how you want. If you want to invest in one gold polish, my favourite is Essie's Good As Gold. It's super shiny, not too streaky and catches the light realistically.
I'd be cautious mixing two types of nail polish at all though! I've tried it before and ended up with a goopy mess that never really dried.
There are a bunch of web sites that give color formulas to replicate different skin colors and metal colors like gold and silver (just do an online search for the specific color you want). But color, alone, isn't what makes metals look like metals. If you simply mix the color, you get a yellowish color for gold-tone metals and a grayish color for silvery metals, that don't look like metals.
What makes metals look like metals is the reflectivity. If you look at the gold nugget in Joachim's answer, it isn't a uniform color, there are wide variations in brightness around a yellowish color hue based on light reflecting from the irregular surface.
Metallic paints sometimes use very fine metal dust to impart not just the characteristic color, but the reflectivity. Sometimes they mix the color from a pallet of non-metallic pigments, and then add something like mica powder to give it some "sparkle" that looks metallic.
In art, metallic media tends to look like scintered metal (metal objects made from compressed metal powder). It looks sparkly matte rather than like a polished metal surface. Sometimes the metal dust or mica isn't uniformly mixed, so you get a little bit of what looks like some surface texture rather than a completely uniform surface.
Unpolished metal, like the nugget in Joachim's picture, is replicated by reproducing the complex patterns of light and dark formed by reflections from the irregular surface. Polished metal is replicated by reproducing the reflections visible on the surface. On flat polished metal, the surface will act like a mirror and you see reflections of nearby objects. On curved polished metal, the reflections will be distorted.
For nail polish color that you just want to look metallic, it would probably be sufficient to mix in a little mica powder (metallic-look or sparkly eye shadow would be an inexpensive source). If your goal is nail art that looks like a metal object, it's a small canvas, but you would need to replicate the color variations and reflections rather than make it sparkly.
Skin color can be mixed if you have white, red, and yellow nail polish. Provided these colours have equal opacity and color strength, you can get a good idea of what the proportions should be here.
For a gold coloured mixture the process is the same, unless you need it to have the luster that is characteristic of gold. If you have silver or another metallic nail polish with such a specular effect, you could try adding yellow to it.
Another option is to combine several yellow hues. Looking at this picture:
You can easily distinct three different hues (by eye, or using photoshop or a similar image editing tool), that can be mixed with the same three colours you would use to create the skin colour.
Uploading the image to an online colour palette creation tool, like coolors.co, you can extract the colors quicker and easier.